We propose an $\alpha$-separable graph Hamiltonian network ($\alpha$-SGHN) that reveals complex interaction patterns between particles in lattice systems. Utilizing trajectory data, $\alpha$-SGHN infers potential interactions without prior knowledge about particle coupling, overcoming the limitations of traditional graph neural networks that require predefined links. Furthermore, $\alpha$-SGHN preserves all conservation laws during trajectory prediction. Experimental results demonstrate that our model, incorporating structural information, outperforms baseline models based on conventional neural networks in predicting lattice systems. We anticipate that the results presented will be applicable beyond the specific on-site and intersite interaction lattices studied, including the Frenkel-Kontorova model, the rotator lattice, and the Toda lattice.

${\mathrm{UO}}_2$ is a crucial nuclear material but its behaviors are elusive due to the impact of superionic diffusion. Herein, we introduce a simple but effective theoretical model to describe the intrinsic superionicity of ${\mathrm{UO}}_2$ at the quantitative level. Our idea stems from a close similarity between superionic crystals and supercooled liquids. Namely, we view ${\mathrm{UO}}_2$ as a randomly pinned hard-sphere fluid in the framework of the elastically collective nonlinear Langevin equation theory. This treatment allows us to fully evaluate the contribution of local, collective, pinning, and screening effects to the molecular dynamics of ${\mathrm{UO}}_2$ without complex computational processes. Finite-temperature factors are considered via volumetric expansion during isobaric heating. On that basis, we satisfactorily explain recent large-scale atomistic simulations on ${\mathrm{UO}}_2$ under various thermodynamic conditions. Our calculations also reveal that ${\mathrm{UO}}_2$ is equivalent to an intermediate glass former. Its structural relaxation, self-diffusion, and shear deformation are strongly correlated near the onset of superionicity. These intimate correlations are reminiscent of the famed Dyre shoving model in the soft-matter community. Our results promise to facilitate the development of diverse energy applications of ${\mathrm{UO}}_2$.

It is well-known that a thin sheet held in a rigid circular clamp has a larger flexural strength than when it is flat. Here, we report that the flexural strength of curved sheets is further increased with a softening of the clamping condition. This unexpected compliance effect relates to the geometrical properties of curvature-induced rigidity that we observe in controlled experiments and further analyze with numerical simulations. In addition, we identify another compliance effect in which opened curved sheets can be more resistant to bending than closed cylinders of same dimensions.

We investigate thermoelastic behavior of nonlinear chains with an instantaneously created temperature profile. We focus on a regime, further referred to as the ballistic thermoelasticity. In this regime, macroscopic strains are small, thermal expansion is linear, conversion of mechanical energy into heat is negligible, and heat transfer is almost ballistic. Equations describing ballistic thermoelasticity of the chains in the continuum limit are solved analytically. Several particular initial temperature profiles are considered to demonstrate peculiarities and limitations of these equations. The main feature of ballistic thermoelasticity is that wave propagation and ballistic heat transfer have the same characteristic timescale. Then, in particular, the quasistatic approximation, having reasonable accuracy in many problems of classical Fourier-law-based thermoelasticity, is irrelevant in the ballistic thermoelasticity. Another peculiarity is the ballistic resonance (BR), i.e., the emergence of mechanical vibrations with an infinitely growing amplitude in the case of sinusoidal initial temperature profile. Using BR as an example, we analyze the importance of dynamical terms in equations of ballistic thermoelasticity and discuss the possibility of observing the BR for initial conditions, corresponding to real experiments. We also show that the BR, previously observed only in the $\alpha$-FPUT chain, is also present in the Lennard-Jones and Toda chains. To demonstrate limitations of the equations of ballistic thermoelasticity, we examine discontinuous and piecewise linear temperature profiles. We show that analytical solutions for strains, corresponding to discontinuous initial temperature profiles, have singularities. For piecewise linear profiles, the analytical solutions are finite and describe simulation results with reasonable accuracy. However the latter is true only if the characteristic length of temperature changes is much larger than the lattice constant.

Understanding the ionization balance of extremely dense plasmas still remains a scientific challenge for both theory and experiment, which is very important in many research fields such as the equation of state, radiative opacity, and thermal and electrical conductivities. In a most recent experiment at the National Ignition Facility, the onset of pressure-driven K-shell delocalization was observed in hot dense Be plasmas [T. Döppner et al., Nature (London) 618, 270 (2023)]. However, all the referenced widely used ionization models can only reproduce part of the experimental data on the ionization state. It is generally regarded that the normal Saha equation is difficult to be applied to the dense plasma regime of, for instance, above a mass density of $10\mathrm{g}/{\mathrm{cm}}^3$ when the interactions between the charged particles and the pressure ionization start to dominate the ionization balance. Herein, we show that the chemical picture of the ionization balance can be extended to an even denser regime up to a density of, for example, $100\mathrm{g}/{\mathrm{cm}}^3$ or higher when the nonideal effects due to the interactions between the electrons and ions and among the electrons themselves and the pressure-induced ionization can be properly considered in a modified Saha equation. An accurate prediction of the ionization potential depression is crucial to depict the transition of the pressure-induced ionization with increasing plasma density. Comparison of our calculated average degree of ionization with the above-mentioned experiment shows good agreement for all the experimental data before and after the K-shell delocalization transition.

In hot dense plasmas, orbital delocalization and relocalization considerably influence the ionization balance, equation of state and radiative properties of matter. A self-consistent plasma screening potential is applied in atomic structure calculations for solid-density Mg plasmas, generated by an x-ray free electron laser (XFEL). As the charge state increases, the $M$-shell orbitals of $K$-hole Mg ions gradually relocalize, beginning with ${\mathrm{Mg}}^{6+}$ at solid density. The level population distributions are determined by solving a time-dependent rate equation using fine-structure level accounting approximations. The predicted $K_{\alpha }$ emission spectra align well with XFEL experiments only when orbital relocalization is carefully accounted for, revealing that the $3d$ orbital of ${\mathrm{Mg}}^{7+}$ is delocalized, consistent with density functional theory calculations.

The motion of photocatalytic silver chloride nanoparticles (AgCl NPs) with radius $R\sim 70\mathrm{nm}$ that use electrolyte self-diffusiophoresis to achieve autonomous propulsion is fully characterized using heterodyne dynamic light scattering, allowing accurate determination of both ballistic and random Brownian diffusion contributions. This technical approach made it possible to reveal the directional self-propulsion of a very large ensemble of light-activated small-size nanoparticles in a 3D spatially nonconfined Brownian environment. Their speeds and direction are easily controlled using an ultraviolet (UV) irradiation external stimulus. We also report the programmable self-assembly and collective behavior of photoactive AgCl NPs.

Negative couplings and suitable initial conditions can induce asymmetric repulsions in feedback loops of odd-numbered overdamped bistable oscillators, allowing them to switch between stable fixed points and produce sustained oscillations that resemble traveling waves [Phys. Rev. E 68, 045102(R) (2003)]. This study shows that changing negative couplings to positive ones can create symmetric attractions among even-numbered overdamped bistable oscillators, leading to similar travelinglike oscillations. We employ a simple two-state model to elucidate the symmetric initial conditions required for these oscillations and estimate the necessary ranges of coupling strength to maintain them. Additionally, we analyze the relationships between oscillation amplitude and frequency regarding the coupling strength and the model parameter, which are consistent with our numerical results. Our findings enhance the understanding of coupling-induced oscillations.

Transport networks are pervasive in nature, often as a result of some optimization processes. A number of theories explain networks exhibiting either loops or tree configurations. On the contrary, an explanation of the coexistence of tree and loop structures remains a challenge unless flow unsteadiness or channel redundancy is introduced. We propose a framework based on a modified channel construction cost, providing coexistence also in steady-state conditions. Extensive simulations support the robustness of our approach. The presence of loops allows flow distribution to approach the theoretical scaling exponent $-1/2$, a result so far not obtained in the single source configuration.

The quest to understand structure-function relationships in networks across scientific disciplines has intensified. However, the optimal network architecture remains elusive, particularly for complex information processing. Therefore, we investigate how optimal and specific network structures form to efficiently solve distinct tasks using a framework of performance-dependent network evolution, leveraging reservoir computing principles. Our study demonstrates that task-specific minimal network structures obtained through this framework consistently outperform networks generated by alternative growth strategies and Erdős-Rényi random networks. Evolved networks exhibit unexpected sparsity and adhere to scaling laws in node-density space while showcasing a distinctive asymmetry in input and information readout node distribution. Consequently, we propose a heuristic for quantifying task complexity from performance-dependently evolved networks, offering valuable insights into the evolutionary dynamics of the network structure-function relationship. Our findings advance the fundamental understanding of process-specific network evolution and shed light on the design and optimization of complex information processing mechanisms, notably in machine learning.

The impact of ion pressure anisotropy on the energy cascade rate of Hall-MHD turbulence with biadiabatic ions and isothermal electrons is evaluated in three-dimensional direct numerical simulations, using the exact (or third-order) law derived by Simon and Sahraoui in 2022. It is shown that pressure anisotropy can enhance or reduce the cascade rate, depending on the scales, in comparison with the prediction of the exact law with isotropic pressure, by an amount that correlates well with pressure anisotropy, $a_p=\frac{p_{\perp }}{p_{\parallel }}\ne 1$, that develops in simulations initialized with an isotropic pressure (${a_p}_0=1$). A simulation with initial pressure anisotropy ${a_p}_0=4$ confirms this trend, exhibiting a stronger impact on the cascade rate, both in the inertial range and at larger scales, close to the forcing scales. Furthermore, a Fourier-based numerical method, to compute exact laws in numerical simulations in the full $({\ell }_{\perp },{\ell }_{\parallel })$ increment plane, is presented.

Disordered systems under applied loading display slow creep flows at finite temperature. Renormalization group arguments predicted that creep proceeds via thermal avalanches of activated events. Recently, thermal avalanches were argued to control the dynamics of liquids near their glass transition. Both theoretical approaches are markedly different. Here we provide a scaling description that seeks to unify dynamical heterogeneities in both phenomena, confirm it in simple models of pinned elastic interfaces, and discuss its experimental implications.

This study examines the dynamics of a tracer particle diffusing in a nonequilibrium medium under stochastic resetting. The nonequilibrium state is induced by harmonic coupling between the tracer and bath particles, generating memory effects with an exponential decay in time. We explore the tracer's behavior under a Poissonian resetting protocol, where resetting does not disturb the bath environment, with a focus on key dynamical behavior and first-passage properties, both in the presence and absence of an external force. The interplay between coupling strength and diffusivity of bath particles significantly impacts both the tracer's relaxation dynamics and search time, with external forces further modulating these effects. Our analysis identifies distinct hot and cold bath particles based on their diffusivities, revealing that coupling to a hot particle facilitates the searching process, whereas coupling to a cold particle hinders it. Using a combination of numerical simulations and analytical methods, this study provides a comprehensive framework for understanding resetting mechanisms in non-Markovian systems, with potential applications to complex environments such as active and viscoelastic media, where memory-driven dynamics and nonequilibrium interactions are significant.

We introduce a random matrix model for the stationary covariance of multivariate Ornstein-Uhlenbeck processes with heterogeneous temperatures, where the covariance is constrained by the Sylvester-Lyapunov equation. Using the replica method, we compute the spectral density of the equal-time covariance matrix characterizing the stationary states, demonstrating that this model undergoes a transition between stable and unstable states. In the stable regime, the spectral density has finite and positive support, whereas negative eigenvalues emerge in the unstable regime. We determine the critical line separating these regimes and show that the spectral density exhibits a power-law tail at marginal stability, with an exponent independent of the temperature distribution. Additionally, we compute the spectral density of the lagged covariance matrix characterizing the stationary states of linear transformations of the original dynamical variables. Our random-matrix model is potentially interesting to understand the spectral properties of empirical correlation matrices appearing in the study of complex systems.

Quantum technologies and experiments often require preparing systems in low-temperature states. Here we investigate cooling schemes using feedback protocols modeled with a quantum Fokker-Planck master equation (QFPME) recently derived by Annby-Andersson et al. [Phys. Rev. Lett. 129, 050401 (2022)]. This equation describes systems under continuous weak measurements, with feedback based on the outcome of these measurements. We apply this formalism to study the cooling and trapping of a harmonic oscillator for several protocols based on position and/or momentum measurements. We find that the protocols can cool the oscillator down to, or close to, the ground state for suitable choices of parameters. Our analysis provides an analytically solvable case study of quantum measurement and feedback and illustrates the application of the QFPME to continuous quantum systems.

We investigate how a constant time delay influences a parametric autoresonant system. This is a nonlinear system driven by a parametrically chirped force with a negative delay feedback that maintains adiabatic phase locking with the driving frequency. This phase locking results in a continuous amplitude growth, regardless of parameter changes. Our study reveals a critical threshold for delay strength; above this threshold, autoresonance is sustained, while below it, autoresonance diminishes. We examine the interplay between time delay and autoresonance stability, using multiscale perturbation methods to derive analytical results, which are corroborated by numerical simulations. Ultimately, the goal is to understand and control autoresonance stability through the time-delay parameters.

A central concern of community ecology is the interdependence between interaction strengths and the underlying structure of the network upon which species interact. In this work we present a solvable example of such a feedback mechanism in a generalized Lotka-Volterra dynamical system. Beginning with a community of species interacting on a network with arbitrary degree distribution, we provide an analytical framework from which properties of the eventual "surviving community" can be derived. We find that highly connected species are less likely to survive than their poorly connected counterparts, which skews the eventual degree distribution towards a preponderance of species with lower degrees. Furthermore, the average abundance of the neighbors of a species in the surviving community is lower than the community average (reminiscent of the famed friendship paradox). Finally, we show that correlations emerge between the connectivity of a species and its interactions with its neighbors. More precisely, we find that highly connected species tend to benefit from their neighbors more than their neighbors benefit from them. These correlations are not present in the initial pool of species and are a result of the dynamics.

We present a generic framework for describing interacting, spinning, active polar particles, aimed at modeling dense cell aggregates, where cells are treated as polar, rotating objects that interact mechanically with one another and their surrounding environment. Using principles from nonequilibrium thermodynamics, we derive constitutive equations for interaction forces, torques, and polarity dynamics. We subsequently use this framework to analyze the spontaneous motion of cell doublets, uncovering a rich phase diagram of collective behaviors, including steady rotation driven by flow-polarity coupling or interactions between polarity and cell position.